class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& matrix) {
        int n = matrix.size();

        vector<vector<int>>dp(n + 1, vector<int>(n + 2, INT_MAX));
        for (int j = 0; j < n + 2; j++) dp[0][j] = 0;
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= n; j++)
                dp[i][j] = min(dp[i - 1][j - 1], min(dp[i - 1][j], dp[i - 1][j + 1])) + matrix[i - 1][j - 1];

        int ret = INT_MAX;
        for (int j = 1; j <= n; j++)
            ret = min(ret, dp[n][j]);

        return ret;
    }
};